Suppose you have \(-x \geq 4\), what happens when you multiply both sides by \(-1\)? You actually get \(x \leq -4\). This doesn't happen with \(=\) because it is sementric... but think about it this way:
\[-x \geq 4 \rightarrow 0\geq 4+x\rightarrow -4 \geq x \rightarrow x\leq -4\]